The rectangle is divided into four parts B, C, D and E. The ratio of Part B to Part C is 7 : 5 and the ratio of Part C to Part D is 3 : 1.
- Find the ratio of Part B to Part C to Part D.
- Given that Part E is 93 cm2 , find the area of the rectangle.
(a)
B |
C |
D |
E |
7x3 |
5x3 |
|
|
|
3x5 |
1x5 |
|
21 u |
15 u |
5 u |
93 cm2 |
Part C is the repeated identity.
LCM of 5 and 3 = 15
Part B : Part C : Part D = 21 : 15 : 5
(b)
Part B + Part C = Half of the rectangle
Part D + Part E = Half of the rectangle
Part B + Part C and Part D + Part E are equal.
Part B + Part C = Part D + Part E
21 u + 15 u = 5 u + 93
21 u + 15 u - 5 u = 93
31 u = 93
1 u = 93 ÷ 31 = 3
Area of the rectangle
= 2 x (5 u + 93)
= 2 x (5 x 3 + 93)
= 2 x (15 + 93)
= 2 x 108
= 216 cm
2 Answer(s): (a) 21 : 15 : 5; (b) 216 cm
2